In the following, simplify using absolute values as necessary. 3{216a6}

Given information: An expression is given as ${\displaystyle \sqrt{3}\left\{216a^6\right\}}$.
Calculations: We have been given an expression is ${\displaystyle \sqrt{3}\left\{216a^6\right\}}$.
For finding the odd and even roots by using the absolute value as necessary, we must know about the power property of exponent i.e.
${\displaystyle {\left(a^m\right)}^n=a^{m\cdot n}}$
${\displaystyle \Rightarrow \sqrt{3}\left\{216a^6\right\}}$ [Simplify the cube root of ${\displaystyle 216a^6}$]
${\displaystyle \Rightarrow \sqrt{3}\left\{{\left(6a^2\right)}^3\right\}}$ [Break the power exponent in the form of ${\displaystyle {\left(a^m\right)}^n=a^{m\cdot n}}$]
${\displaystyle \Rightarrow 6a^2}$ [${\displaystyle \sqrt{n}\left\{a^n\right\}=a}$, if the value of n is odd.]
Thus, index value of ${\displaystyle \sqrt{3}\left\{216a^6\right\}}$ is odd.
Hence, the simplification of ${\displaystyle \sqrt{3}\left\{216a^6\right\}is6a^2}$